Eevee renders in gray and workbench renders in colors
Did you just set for Viewport Render Color in your mesh?



That is not how EEVEE and cycles retrieve color. They have nothing to do with final render in both render engine. It just change your viewport color which is faster and simple for easy render task. Instead of that one, you should assign a material to your mesh, and change the color of that shader (principled shader perhaps?). Then you will get the color in EEVEE and cycles.